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// Set OVERLAPPING to 1 in order to fill in the edges of the box, with
// c endcaps and b overlapping a. With the proper choice of parameters,
// (setting rim slds to sld, core sld to solvent, rim thickness to thickness
// and subtracting 2*thickness from length, this should match the hollow
// rectangular prism.) Set it to 0 for the documented behaviour.
#define OVERLAPPING 0
static double
form_volume(double length_a, double length_b, double length_c,
double thick_rim_a, double thick_rim_b, double thick_rim_c)
{
return
#if OVERLAPPING
// Hollow rectangular prism only includes the volume of the shell
// so uncomment the next line when comparing. Solid rectangular
// prism, or parallelepiped want filled cores, so comment when
// comparing.
//-length_a * length_b * length_c +
(length_a + 2.0*thick_rim_a) *
(length_b + 2.0*thick_rim_b) *
(length_c + 2.0*thick_rim_c);
#else
length_a * length_b * length_c +
2.0 * thick_rim_a * length_b * length_c +
2.0 * length_a * thick_rim_b * length_c +
2.0 * length_a * length_b * thick_rim_c;
#endif
}
static double
radius_from_excluded_volume(double length_a, double length_b, double length_c,
double thick_rim_a, double thick_rim_b, double thick_rim_c)
{
double r_equiv, length;
double lengths[3] = {length_a+thick_rim_a, length_b+thick_rim_b, length_c+thick_rim_c};
double lengthmax = fmax(lengths[0],fmax(lengths[1],lengths[2]));
double length_1 = lengthmax;
double length_2 = lengthmax;
double length_3 = lengthmax;
for(int ilen=0; ilen<3; ilen++) {
if (lengths[ilen] < length_1) {
length_2 = length_1;
length_1 = lengths[ilen];
} else {
if (lengths[ilen] < length_2) {
length_2 = lengths[ilen];
}
}
}
if(length_2-length_1 > length_3-length_2) {
r_equiv = sqrt(length_2*length_3/M_PI);
length = length_1;
} else {
r_equiv = sqrt(length_1*length_2/M_PI);
length = length_3;
}
return 0.5*cbrt(0.75*r_equiv*(2.0*r_equiv*length + (r_equiv + length)*(M_PI*r_equiv + length)));
}
static double
radius_from_volume(double length_a, double length_b, double length_c,
double thick_rim_a, double thick_rim_b, double thick_rim_c)
{
const double volume = form_volume(length_a, length_b, length_c, thick_rim_a, thick_rim_b, thick_rim_c);
return cbrt(volume/M_4PI_3);
}
static double
radius_from_crosssection(double length_a, double length_b, double thick_rim_a, double thick_rim_b)
{
const double area_xsec_paral = length_a*length_b + 2.0*thick_rim_a*length_b + 2.0*thick_rim_b*length_a;
return sqrt(area_xsec_paral/M_PI);
}
static double
radius_effective(int mode, double length_a, double length_b, double length_c,
double thick_rim_a, double thick_rim_b, double thick_rim_c)
{
switch (mode) {
default:
case 1: // equivalent cylinder excluded volume
return radius_from_excluded_volume(length_a, length_b, length_c, thick_rim_a, thick_rim_b, thick_rim_c);
case 2: // equivalent volume sphere
return radius_from_volume(length_a, length_b, length_c, thick_rim_a, thick_rim_b, thick_rim_c);
case 3: // half outer length a
return 0.5 * length_a + thick_rim_a;
case 4: // half outer length b
return 0.5 * length_b + thick_rim_b;
case 5: // half outer length c
return 0.5 * length_c + thick_rim_c;
case 6: // equivalent circular cross-section
return radius_from_crosssection(length_a, length_b, thick_rim_a, thick_rim_b);
case 7: // half outer ab diagonal
return 0.5*sqrt(square(length_a+ 2.0*thick_rim_a) + square(length_b+ 2.0*thick_rim_b));
case 8: // half outer diagonal
return 0.5*sqrt(square(length_a+ 2.0*thick_rim_a) + square(length_b+ 2.0*thick_rim_b) + square(length_c+ 2.0*thick_rim_c));
}
}
static void
Fq(double q,
double *F1,
double *F2,
double core_sld,
double arim_sld,
double brim_sld,
double crim_sld,
double solvent_sld,
double length_a,
double length_b,
double length_c,
double thick_rim_a,
double thick_rim_b,
double thick_rim_c)
{
// Code converted from functions CSPPKernel and CSParallelepiped in libCylinder.c
// Did not understand the code completely, it should be rechecked (Miguel Gonzalez)
// Code is rewritten, the code is compliant with Diva Singh's thesis now (Dirk Honecker)
// Code rewritten; cross checked against hollow rectangular prism and realspace (PAK)
const double half_q = 0.5*q;
const double tA = length_a + 2.0*thick_rim_a;
const double tB = length_b + 2.0*thick_rim_b;
const double tC = length_c + 2.0*thick_rim_c;
// Scale factors
const double dr0 = (core_sld-solvent_sld);
const double drA = (arim_sld-solvent_sld);
const double drB = (brim_sld-solvent_sld);
const double drC = (crim_sld-solvent_sld);
// outer integral (with gauss points), integration limits = 0, 1
// substitute d_cos_alpha for sin_alpha d_alpha
double outer_sum_F1 = 0; //initialize integral
double outer_sum_F2 = 0; //initialize integral
for( int i=0; i<GAUSS_N; i++) {
const double cos_alpha = 0.5 * ( GAUSS_Z[i] + 1.0 );
const double mu = half_q * sqrt(1.0-cos_alpha*cos_alpha);
const double siC = length_c * sas_sinx_x(length_c * cos_alpha * half_q);
const double siCt = tC * sas_sinx_x(tC * cos_alpha * half_q);
// inner integral (with gauss points), integration limits = 0, 1
// substitute beta = PI/2 u (so 2/PI * d_(PI/2 * beta) = d_beta)
double inner_sum_F1 = 0.0;
double inner_sum_F2 = 0.0;
for(int j=0; j<GAUSS_N; j++) {
const double u = 0.5 * ( GAUSS_Z[j] + 1.0 );
double sin_beta, cos_beta;
SINCOS(M_PI_2*u, sin_beta, cos_beta);
const double siA = length_a * sas_sinx_x(length_a * mu * sin_beta);
const double siB = length_b * sas_sinx_x(length_b * mu * cos_beta);
const double siAt = tA * sas_sinx_x(tA * mu * sin_beta);
const double siBt = tB * sas_sinx_x(tB * mu * cos_beta);
#if OVERLAPPING
const double f = dr0*siA*siB*siC
+ drA*(siAt-siA)*siB*siC
+ drB*siAt*(siBt-siB)*siC
+ drC*siAt*siBt*(siCt-siC);
#else
const double f = dr0*siA*siB*siC
+ drA*(siAt-siA)*siB*siC
+ drB*siA*(siBt-siB)*siC
+ drC*siA*siB*(siCt-siC);
#endif
inner_sum_F1 += GAUSS_W[j] * f;
inner_sum_F2 += GAUSS_W[j] * f * f;
}
// now complete change of inner integration variable (1-0)/(1-(-1))= 0.5
// and sum up the outer integral
outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * 0.5;
outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * 0.5;
}
// now complete change of outer integration variable (1-0)/(1-(-1))= 0.5
outer_sum_F1 *= 0.5;
outer_sum_F2 *= 0.5;
//convert from [1e-12 A-1] to [cm-1]
*F1 = 1.0e-2 * outer_sum_F1;
*F2 = 1.0e-4 * outer_sum_F2;
}
static double
Iqabc(double qa, double qb, double qc,
double core_sld,
double arim_sld,
double brim_sld,
double crim_sld,
double solvent_sld,
double length_a,
double length_b,
double length_c,
double thick_rim_a,
double thick_rim_b,
double thick_rim_c)
{
// cspkernel in csparallelepiped recoded here
const double dr0 = core_sld-solvent_sld;
const double drA = arim_sld-solvent_sld;
const double drB = brim_sld-solvent_sld;
const double drC = crim_sld-solvent_sld;
const double tA = length_a + 2.0*thick_rim_a;
const double tB = length_b + 2.0*thick_rim_b;
const double tC = length_c + 2.0*thick_rim_c;
const double siA = length_a*sas_sinx_x(0.5*length_a*qa);
const double siB = length_b*sas_sinx_x(0.5*length_b*qb);
const double siC = length_c*sas_sinx_x(0.5*length_c*qc);
const double siAt = tA*sas_sinx_x(0.5*tA*qa);
const double siBt = tB*sas_sinx_x(0.5*tB*qb);
const double siCt = tC*sas_sinx_x(0.5*tC*qc);
#if OVERLAPPING
const double f = dr0*siA*siB*siC
+ drA*(siAt-siA)*siB*siC
+ drB*siAt*(siBt-siB)*siC
+ drC*siAt*siBt*(siCt-siC);
#else
const double f = dr0*siA*siB*siC
+ drA*(siAt-siA)*siB*siC
+ drB*siA*(siBt-siB)*siC
+ drC*siA*siB*(siCt-siC);
#endif
return 1.0e-4 * f * f;
}
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